Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.
 M.I. Rabinovich, P. Varona, A.I. Selverston, H.D.I. Abarbanel, ”Dynamical principles in neuroscience”, Reviews of Modern Physics, vol.78, no.4, pp.1213–1265, Nov. 2006.
 J. Wojcik, A. Shilnikov, ”Voltage interval mappings for activity transitions in neuron models for elliptic bursters”, Physica D: Nonlinear Phenomena, vol.240, no.14, pp.1164-1180, Apr. 2011.
 H.A. Braun, J. Schwabedal, M. Dewald, C. Finke, S. Postnova, M.T. Huber, B. Wollweber, H. Schneider, M.C. Hirsch, K. Voigt, U. Feudel, F. Moss, ”Noise-induced precursors of tonic-to-bursting transitions in hypothalamic neurons and in a conductance-based model”, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.21, no.4, 047509, Dec. 2011.
 A.L. Hodgkin, A.F. Huxley, ”A quantitative description of membrane current and application to conduction and excitation in nerve”, Journal of Physiology vol.117, no.4, pp.500–544, Aug. 1952.
 E.M. Izhikevich, ”Simple Model of Spiking Neurons”, IEEE Transactions on Neural Networks, vol.14, no.6, pp. 1569–1572, Nov. 2003.
 E.M. Izhikevich, ”Which Model to Use for Cortical Spiking Neurons?”, IEEE Transactions on Neural Networks, vol.15, no.5, pp.1063–1070, Sep. 2004.
 K. Aihara, H. Suzuki, ”Theory of hybrid dynamical systems and its applications to biological and medical systems”, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences vol.368, no.1930, pp.4893–4914, May 2010.
 S. Coombes, R. Thul, K.C.A. Wedgwood, ”Nonsmooth dynamics in spiking neuron models”, Physica D: Nonlinear Phenomena, vol.241, no.22, pp.2042–2057, Nov. 2012.
 W.J. Freeman, ”Tutorial on neurobiology: from single neurons to brain chaos”, International journal of bifurcation and chaos, vol.2, no.3, pp.451–482, Sept. 1992.
 N. Schweighofer, K. Doya, H. Fukai, J.V. Chiron, T. Furukawa, M. Kawato, ”Chaos may enhance information transmission in the inferior olive”, Proceedings of the National Academy of Sciences, vol.101, no.13, pp.4655–4660, Sept. 2004.
 S. Nobukawa, H. Nishimura, ”Characteristic of Signal Response in Coupled Inferior Olive Neurons with Velarde-Llinás Model”, In SICE Annual Conference, pp.1367–1374, Sept. 2013.
 I. T. Tokuda, H. Hoang, N. Schweighofer, M. Kawato, ”Adaptive coupling of inferior olive neurons in cerebellar learning” Neural Networks, vol.47, pp.42–50, Dec. 2013.
 A. Tamura, T. Ueta, S. Tsuji, ”Bifurcation analysis of Izhikevich neuron model”, Dynamics of continuous, discrete and impulsive systems, Series A: mathematical analysis vol.16, no.6, pp.849–862, 2009.
 D. Itou, T. Ueta, K. Aihara, ”Bifurcation Analysis with Threshold Values for Interrupt Autonomous Systems”, IEICE Trans. Fundamentals, vol.94-A, no.8, pp.596–603, Aug. 2011.
 S. Nobukawa, H. Nishimura, T. Yamanishi, J.-Q. Liu, ”Chaotic Dynamical States in Izhikevich Neuron Model”, Emerging Trends in Computational Biology, Bioinformatics, and Systems Biology - Algorithms and Software Tools, Elsevier/MK (to be published).
 N. Sugiura, K. Fujiwara, R. Hosakawa, K. Jin’no, T. Ikeguchi, ”Estimation of Lyapunov exponents of chaotic response in the Izhikevich neuron model”, IEICE Technical report NLP2013-113, pp.1–6, Dec. 2013
 F. Bizzarri, A. Brambilla, G.S. Gajani, ”Lyapunov exponents computation for hybrid neurons”, J. Comput. Neurosci. vol.35, no.2, pp.201–212, Feb. 2013.
 S. Nobukawa, H. Nishimura, T. Yamanishi, J.-Q. Liu, ”Analysis of Routes to Chaos in Izhikevich Neuron Model with Resetting Process”, Proc. The 7th International Conference on Soft Computing and Intelligent Systems, The 15th International Symposium on Advanced Intelligent Systems (SCIS-ISIS2014), pp.813–818, Dec. 2014.
 A.C. Hindmarsh, P.N. Brown, K.E. Grant, S.L. Lee, R. Serban, D.E. Shumaker, C.S. Woodward, ”SUNDIALS: Suite of nonlinear and differential/algebraic equation solvers”, ACM Transactions on Mathematical Software, vol.31, no.3, pp.363–396, Sep. 2005.
 M.D. Bernardo (Ed.), Piecewise-smooth dynamical systems: theory and applications, Springer, 2008.
 T.S. Parker, L.O. Chua, Practical Numerical Algorithms for Chaotic Systems, Springer-Verlag New York Inc, 1989.
 S. Zambrano, I.P. Mario, J.M. Seoane, M.A. Sanjun, S. Euzzor, A. Geltrude, R. Meucci, F.T. Arecchi, ”Synchronization of uncoupled excitable systems induced by white and coloured noise”, New Journal of Physics, vol.12, no.5, 053040, May 2010.
 H. Nagashima, Y. Baba, Introduction to chaos: physics and mathematics of chaotic phenomena, CRC Press, 1998.
 P. Berge, Y. Pomeau, C. Vidal, Order in chaos, The Deterministic Approach to Turbulence, 1984.